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Absolute end points of irreducible continua

Janusz Jerzy Charatonik — 1993

Mathematica Bohemica

A concept of an absolute end point introduced and studied by Ira Rosenholtz for arc-like continua is extended in the paper to be applied arbitrary irreducible continua. Some interrelations are studied between end points, absolute end points and points at which a given irreducible continuum is smooth.

Mappings related to confluence

Janusz Jerzy Charatonik — 1996

Archivum Mathematicum

Necessary and sufficient conditions are found in the paper for a mapping between continua to be monotone, confluent, semi-confluent, joining, weakly confluent and pseudo-confluent. Three lists of these conditions are presented. Two are formulated in terms of components and of quasi-components, respectively, of connected closed subsets of the range space, while the third one in terms of connectedness between subsets of the domain space. Some basic relations concerning these concepts are studied.

AANR spaces and absolute retracts for tree-like continua

Janusz Jerzy CharatonikJanusz R. Prajs — 2005

Czechoslovak Mathematical Journal

Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, λ -dendroids, dendroids, arc-like continua and arc-like λ -dendroids is an approximative absolute...

On self-homeomorphic dendrites

Janusz Jerzy CharatonikPaweł Krupski — 2002

Commentationes Mathematicae Universitatis Carolinae

It is shown that for every numbers m 1 , m 2 { 3 , , ω } there is a strongly self-homeomorphic dendrite which is not pointwise self-homeomorphic. The set of all points at which the dendrite is pointwise self-homeomorphic is characterized. A general method of constructing a large family of dendrites with the same property is presented.

Homotopy properties of curves

Janusz Jerzy CharatonikAlejandro Illanes — 1998

Commentationes Mathematicae Universitatis Carolinae

Conditions are investigated that imply noncontractibility of curves. In particular, a plane noncontractible dendroid is constructed which contains no homotopically fixed subset. A new concept of a homotopically steady subset of a space is introduced and its connections with other related concepts are studied.

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